A wide variety of different types of storage systems are known. For example, some storage systems are configured to include multiple storage tiers, with different ones of the tiers providing different levels of input-output (IO) performance or other characteristics. In such storage systems, data may be moved from one tier to another within a given storage system based on access frequency of the data or other factors. These and other types of storage systems may be shared by multiple host devices of a compute cluster. However, problems can arise in such arrangements in that it can be unduly difficult to coordinate state transitions of multiple host devices in implementing data services involving the storage system.